ATLAS dipolar flow

1. ATLAS dipolar flow ATLAS event-by-event vn Jiangyong Jia for the ATLAS Collaboration https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2012-114/ Quark Matter 2012 Aug 13th- Aug 18th

2. Motivation Detailed study of v1-v6

3. Motivation Singles Pairs Foreground Background

4. Motivation Singles Pairs Foreground Background

5. Motivation Rich event-by-event patterns for both vn and Φn! Singles Pairs Foreground Background

6. Motivation Rich event-by-event patterns for both vn and Φn! Foreground Background For results on Φn correlations, see S. Mohapatra parallel 7D Fri.

7. Motivation Unfold for final multiplicity effects (mainly). The key is response function: Foreground Background

8. ATLAS detector η<0 η>0 Inner detector Tracks |η|<2.5 Tracks in Inner Detector(ID) divided into subevents with flexible η ranges! Pb+Pb data from fall 2010 (48 M events)

9. Obtaining single particle distribution Efficiency weight applied track by track as function of pT and η • Ideal detector: • Correct for acceptance & efficiency:

10. Flow vector distribution & smearing Observed EbE flow vector distribution: Smeared around the true flow vector: 

11. Determining response function η<0 η>0 • Smearing function is purely Gaussian • Response function obtained by integrating out azimuth angle Estimated by the correlation between “symmetric” subevents

12. Bayesian unfolding • unfolding algorithm as implemented in the RooUnfold • True (“cause” c or vn) vs measured distribution (“effect” e or vnobs) Denote response function • Unfolding matrix M is determined via iterative procedure • Prior, c0, can be chosen as input vnobs distribution or it can be chosen to be closer to the truth by a simple rescaling according to the EP vn • Number of iterations Niter adjusted according to sample statistics and binning.

13. Basic unfolding performance: v2, 20-25% Converges within a few % for Niter=8, small improvements for larger Niter.

14. Dependence on prior: v4 20-25% Despite different initial distribution, all converged for Niter=64 Wide prior converges from above, narrow prior converges from below! Constraining the residual non-convergence

15. Compare to unfolding for half-ID: 20-25% Residual non-convergence of half-ID Agrees within a few % in most cases, can be larger in the tails reflects the non-convergence of half-ID (since width of its response function is √2 wider)

16. v2-v4 probability distributions p(vn) distributions with shape uncertainty only Overlaid with Gaussian function adjust to the same mean (curves)

17. Unfolding in different pT ranges: 20-25% Hydrodynamic response ~ independent of pT. Distributions for higher pT bin is broader, but they all have ~same reduced shape  unfolding is robust.

18. Centrality (Npart) dependence of relative widths n=2 n=2 Dotted lines indicate Gaussian limit 0.523 v2: Gaussian in 0-2% centrality, reach 0.34±0.02 for 20-30%

19. Centrality (Npart) dependence of relative widths n=2 n=3 n=4 v2: Gaussian in 0-2% centrality, reach 0.34±0.02 for 20-30% v3-v4: Gaussian for full centrality range.

20. Compare to vnEP results Confirmed!! n=3 n=4 20 n=2 Dotted lines indicate the Gaussian limit Expectations:

21. Hydrodynamic response? For Glauber and CGC mckln 3.46 0-1% 5-10% 20-25% 55-60% 30-35% 40-45% Both models fail describing p(v2) across the full centrality range • Check: Rescale εn distribution to the mean of data

22. How about v3? and v4? 0-1% 5-10% 20-25% 55-60% 30-35% 40-45% Non-linear responses Good agreement except in peripheral collisions, but this could be trivial, since all Gaussian functions have same reduced shape. Similar observation for v4

23. Summary • We measured event-by-event probability distribution of v2-v4 in various centrality: p(vn). • Distributions are Gaussian for v2 in central collisions, and for v3 and v4 in all centrality ranges. • Also supported by the values of ratio • The reduced shape has no pT dependence, hydro response indept of pT • Event plane vn is consistent with • p(v2) is inconsistent with p(ε2) from both Glauber &MC-KLN model. • Provides direct constraints on understanding the hydrodynamic response to initial geometry fluctuations.

24. Back up

25. Glauber or MC-KLN? Glauber MC-KLN Same as the dashed lines from left figure… MC-KLN works better in more central collisions Glauber better in more peripheral collisions

26. Non-flow from short range correlations? η<0 η>0 • Use to to estimate . is Gaussian!! • Nonflow small or number of sources responsible for short-range correlations multiplicity and they are not correlated between the subevents. • True for resonance decays, Bose-Einstein correlation, and single jets? • Non-flow effects is included in response function and unfolded away? • Influence of non-flow to 2PC is different from single unfolding, and for different gaps. But consistent results are observed (see next).

27. Method 2—unfolding EbE two-particle correlation η<0 η>0 • Define observed vn from correlation analysis as: • Term “Bn” is essential! it captures some statistical fluctuations. • The 2PC response function obtained trivially from EbE pair correlation between two symmetric subevents

28. Compare with 2PC unfolding: 20-25% • vnobs,2PC is broader than vnobs, but converges to the same answer • Residual non-convergence mainly due to 2PC unfolding

29. Compare single & 2PC unfolding with η gaps

30. Response function for single and 2PC broader than for small vn. approach each other at for large vn.

31. Basic unfolding performance: v4, 20-25% • More iterations in peripheral collisions and for v3 and v4 • bulk region is converged, both unfolded and refolded, for Niter = 32, but the tails still exhibit some small changes up to Niter = 64. • Statistical error approaches √N for 64<Niter<128 (thanks to large sample stat.). • The differences are always less than 5% between Niter 64 and 128

32. Dependence on prior: v2 20-25% Converge for Niter=8

33. Dependence on prior: v2 20-25% Converge for Niter=8

34. v4 comparison with eccentricity 0-1% 5-10% 20-25% 55-60% 30-35% 40-45% Non-linear responses